1. Field of the Invention
This invention relates generally to a wave front sensor, and more particularly, to a wave front sensor that employs a hybrid combination of a tilt sensor and a curvature sensor to provide an enhanced reconstruction of the phase of the wave front.
2. Discussion of the Related Art
Light from a distant source is typically collimated when it reaches a detector that is being used to sense the light. However, the various beam wavelets at the beam wave front are usually not in temporal coherence, which causes blurriness and distortion of the light beam. In particular, there are phase differences across the wave front of the beam causing the distortion. For example, light from a star looks fuzzy or blurry when it reaches the Earth. Additionally , the optical systems used for optical sensing also cause distortion of the beam wave front. Therefore, wave front sensing has been employed to measure the phase difference across the wave front and improve the performance of optical systems by correcting the phase to reduce beam distortion. Wave front sensing is routinely used in astronomy applications, as well as other engineering disciplines, such as high energy lasers and space surveillance.
Two conventional techniques are known in the art for providing beam wave front sensing. One technique includes determining tilt or slope measurements of the beam wave front using Hartman-Schack sensors. The article Fried, David L., xe2x80x9cLeast-square fitting a wave-front distortion estimate to an array of phase-difference measurements,xe2x80x9d J. Opt. Soc. Am., Vol. 67, No. 3, March, 1977, pgs. 370-375 discusses one of the first known techniques for providing tilt measurements of a beam wave front. In one design, the light is directed through an array of lenslets that focus individual portions of the wave front in the direction determined by their slope. Algorithms are then employed that reconstruct the phase of the wave front by minimizing the least squares error between the observed phase gradient (tilt) and its computed value.
The other known technique for providing beam wave front sensing includes determining curvature measurements of the wave front using intensity sensors. The article Roddier, Francois, xe2x80x9cCurvature Sensing and Compensation: A New Concept in Adaptive Optics,xe2x80x9d Applied Optics, Vol. 27, No. 7, Apr. 1, 1988, pgs. 1223-1225 is one of the original discussions on determining curvature measurements of a beam wave front. Curvature measurements are computed from differences and ratios of the measured intensities of the wave front. The phase is then recovered by solving Laplace""s equation with the right hand side equal to the measured curvature.
Wave front sensing using tilt measurements or intensity measurements present different advantages and drawbacks in various situations. First, these techniques have different sensitivities to the spatial frequency of the phase to be recovered. For example, for correction through atmospheric turbulence with Kolmogorov statistics, the spectrum of the phase of the wave front behaves as k to the power (xe2x88x92{fraction (11/3)}), so that the tilt of the phase of the wave front has a spectrum in k to the power (xe2x88x92{fraction (5/3)}) and the curvature of the phase has a spectrum in k to the power of (⅓). Therefore, the measured tilts are highly correlated and very sensitive to low spatial frequencies. On the other hand, curvature measurements are weakly correlated, especially at low frequencies.
Second, these techniques have a different behavior of the mean-square error as a function of the number of sub-apertures. For Hartman-Schack sensors, this error grows logarithmically, whereas for curvature measurements it grows linearly. Thus, for a large number of sub-apertures, Hartman-Schack sensors are clearly favorable.
Finally, the two methods handle scintillations differently. For Hartman-Schack sensors, scintillation effects are a genuine problem. Curvature sensors, however, alleviate the problem of scintillation since the curvature is derived from the difference of intensities on two planes that are symmetrical with respect to the focal plane of a lens so that the scintillation effects tend to cancel out.
Because the two known techniques of determining wave front sensing have advantages and disadvantages in different areas as described above, a wave front sensing technique that employs both types of techniques would benefit from their advantages, and the disadvantages would be minimized. It is therefore an object of the present invention to provide such a wave front sensing system.
In accordance with the teachings of the present invention, a hybrid curvature/tilt wave front sensor is disclosed that determines both tilt measurements and curvature measurements of the wave front of a light beam. The light beam is split into a first path and a second path. The light beam on the first path is directed to a tilt sensor employing a lenslet array having a plurality of lenses. The lenses focus separate portions of the wave front onto a charged coupled device (CCD) that provides local intensity measurements. These are used by a computer to infer tilt measurements.
The light beam on the second path is directed to a curvature sensor that includes a pair of CCDs positioned at the same distance before and after the focal plane of a lens. The intensity measurement of the beam at these locations is sent to the computer which generates curvature measurements of the beam wave front. Algorithms are employed in the computer to determine the wave front phase based on the tilt and curvature measurements.
Additional objects, advantages and features of the present invention will become apparent from the following description and appended claims, taken in conjunction with the accompanying drawings.